Module III·Article III·~10 min read
Revenue and Profit Maximization
Costs, Production, and Profit Maximization
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Revenue and Profit Maximization
Types of Revenue
To make decisions about pricing and production volume, a firm needs to understand three types of revenue.
Total Revenue (TR)
TR = P × Q — price multiplied by the quantity sold.
This is the most intuitive indicator: how much money the firm receives from selling all its products. But by itself, TR says little about profitability — to gauge that, it must be compared to costs.
Average Revenue (AR)
AR = TR / Q = P — revenue per unit of product, which always equals the price.
The AR curve is the demand curve for the firm's product. This is logical: the price at which the firm sells its product is determined by the demand for its output.
Marginal Revenue (MR)
MR = ΔTR / ΔQ — additional revenue from selling one more unit of output.
For a price taker in a perfectly competitive market: MR = AR = P. The firm can sell any quantity at the market price, so each additional unit brings the same revenue.
For a price maker — a firm with market power: MR < AR. To sell one more unit, the firm must lower the price on all units (if it does not use price discrimination). Therefore, the additional revenue from selling one more unit is less than the price.
Numerical Example: MR for a Price Maker
| Q | P (RUB) | TR (RUB) | MR (RUB) |
|---|---|---|---|
| 1 | 100 | 100 | 100 |
| 2 | 90 | 180 | 80 |
| 3 | 80 | 240 | 60 |
| 4 | 70 | 280 | 40 |
| 5 | 60 | 300 | 20 |
| 6 | 50 | 300 | 0 |
| 7 | 40 | 280 | -20 |
Note: at Q = 2, the price goes down from 100 to 90, and TR increases from 100 to 180. MR = 80, which is less than the price (90). Why? Because the firm not only sells the second unit for 90, but also loses 10 rubles on the first unit (which was previously sold for 100, and now also for 90). MR = 90 - 10 = 80.
At Q = 6, MR = 0: the extra unit does not bring additional revenue. This is the maximum point of TR.
At Q = 7, MR < 0: the extra unit decreases total revenue. No rational firm will produce in this range.
Price Taker vs. Price Maker
Price Taker
A firm in a perfectly competitive market:
- Sells an identical (homogeneous) product, indistinguishable from competitors’ output
- Holds an insignificant market share
- Cannot influence the market price
- “Sees” a horizontal demand curve: D = AR = MR = P
Example: A farmer growing wheat. The world price of wheat is determined by global supply and demand. An individual farmer cannot influence it: he sells as much as he can at the market price. If he tries to set a price above the market — nobody will buy (there are thousands of other farmers with identical wheat). If he sets a price below — he just loses money (he can sell everything at the market price anyway).
Price Maker
A firm with market power (monopoly, oligopoly, monopolistic competition):
- Sells a differentiated or unique product
- Has a significant share of the market
- Can influence price (by setting output or directly setting price)
- “Sees” a downward-sloping demand curve: MR < AR = P
Example: Apple — a price maker in the smartphone market. The iPhone is a differentiated product with a strong brand and no perfect substitutes. Apple sets the price based on demand and its strategy. If Apple wants to sell more iPhones, it must lower the price — so its demand curve slopes downward.
Profit Maximization: the MR = MC Rule
Rule Logic
Profit is the difference between total revenue and total costs: π = TR - TC. The firm maximizes profit by choosing the production level Q* that maximizes the difference between TR and TC.
Marginal analysis shows this is achieved at MR = MC:
- If MR > MC → producing one more unit increases profit (additional revenue exceeds additional cost) → output should be increased
- If MR < MC → producing one more unit decreases profit → output should be reduced
- If MR = MC → profit is maximized (or losses minimized)
Detailed Numerical Example
A firm with market power (price maker):
| Q | P (RUB) | TR | TC | Profit (π) | MR | MC |
|---|---|---|---|---|---|---|
| 0 | — | 0 | 100 | -100 | — | — |
| 1 | 200 | 200 | 150 | 50 | 200 | 50 |
| 2 | 180 | 360 | 190 | 170 | 160 | 40 |
| 3 | 160 | 480 | 240 | 240 | 120 | 50 |
| 4 | 140 | 560 | 310 | 250 | 80 | 70 |
| 5 | 120 | 600 | 400 | 200 | 40 | 90 |
| 6 | 100 | 600 | 520 | 80 | 0 | 120 |
| 7 | 80 | 560 | 670 | -110 | -40 | 150 |
Analysis:
At Q = 1-3: MR > MC → each unit adds to profit → output should be increased. At Q = 4: MR (80) > MC (70) → still profitable, but the difference is small. Profit is maximized: 250 RUB. At Q = 5: MR (40) < MC (90) → the 5th unit reduces profit (loss of 50 RUB) → should not produce it.
Optimal output: Q = 4*, price: P = 140 RUB*, maximum profit: 250 RUB.
Note: MR = MC does not mean “MR exactly equals MC.” In a discrete case, the optimum is the last unit at which MR ≥ MC.
Important Clarification: Normal and Economic Profit
-
Normal profit — the minimum profit needed for a firm to stay in the industry. It is included in costs (as implicit costs — the entrepreneur’s opportunity costs). If a firm earns normal profit, economic profit = 0.
-
Economic profit — profit above normal profit. This is a “bonus” that attracts new firms to the industry (in the absence of entry barriers).
-
Losses — economic profit is negative. The firm earns less than necessary to cover all costs (including normal profit).
Shutdown Decision
Even if a firm is incurring losses, it does not always mean it should immediately stop operating. The shutdown decision in the short run depends on the relationship between price and average variable cost.
Decision Logic
In the short run, the firm bears fixed costs (FC) regardless of whether it operates or not. If it shuts down, its loss equals FC. Therefore, the question: is it better to operate (even at a loss) or to shut down?
-
If P > AVC (price covers variable costs): the firm should continue operating. Each unit sold contributes to covering fixed costs. Losses when operating are less than when shutting down.
-
If P < AVC (price does not even cover variable costs): the firm should shut down. Each unit sold increases losses. It is better to bear only fixed costs.
-
If P = AVC: the firm is at the shutdown point (indifference point) — it is indifferent to operating or shutting down (losses are the same).
Numerical Example: Restaurant in Crisis
Restaurant "Uyut" has the following costs:
- FC = 500,000 RUB/month (rent, manager’s salary, insurance)
- AVC = 800 RUB/dish (ingredients, chef’s piecework pay, electricity)
- Average price per dish = 1,000 RUB
- Sells 1,000 dishes per month
Current situation:
- TR = 1,000 × 1,000 = 1,000,000 RUB
- VC = 800 × 1,000 = 800,000 RUB
- TC = 500,000 + 800,000 = 1,300,000 RUB
- Loss = 1,000,000 - 1,300,000 = -300,000 RUB
The restaurant operates at a loss. But should it shut down?
If it shuts down: loss = FC = -500,000 RUB (rent still must be paid under the contract). If it continues operating: loss = -300,000 RUB
Continuing to operate is preferable, because P (1,000) > AVC (800). Each dish sold contributes 200 RUB toward covering fixed costs (1,000 - 800 = 200). For the month: 200 × 1,000 = 200,000 RUB — this amount partially offsets fixed costs.
Now imagine that during lockdown, the number of customers dropped to 200 dishes per month, and the restaurant had to lower the price to 700 RUB/dish to attract anyone:
- TR = 700 × 200 = 140,000 RUB
- VC = 800 × 200 = 160,000 RUB
- Loss when operating = 140,000 - (500,000 + 160,000) = -520,000 RUB
- Loss when shutting down = -500,000 RUB
Now P (700) < AVC (800). Each dish sold increases losses by 100 RUB. The restaurant should shut down — the losses will be smaller.
Real Examples of Shutdown Decisions
Airlines during COVID-19. In spring 2020, demand for air travel collapsed by 90%. Many airlines faced a choice: fly nearly empty planes or ground them. The calculation was marginal: if the revenue from a flight covered at least variable costs (fuel, airport handling, crew wages), it made sense to fly. If not — the plane stayed on the ground. Many airlines cut flight numbers by 80–90%, keeping only routes where P > AVC.
Oil industry in 2020. When oil prices fell below $20 per barrel, many oil wells were temporarily shut down: their variable extraction costs (pumping, transporting, initial processing) exceeded revenue. Wells with low variable costs (for example, in Saudi Arabia, where extraction costs $3–5 per barrel) remained open. Wells with high variable costs (such as some shale wells in the USA with costs of $30–40 per barrel) were closed until prices recovered.
Long-term Decision
In the long run, all costs are variable. Therefore, the condition to continue operating in the long run is stricter:
- If P ≥ AC → the firm earns normal or economic profit → remains in the industry
- If P < AC → the firm incurs economic losses → exits the industry
This explains why even profitable (in a short-run sense) firms may leave the industry: if their profit is below normal (i.e., less than what the entrepreneur could earn in another industry), it is rational to switch to a more profitable activity.
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